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Statistica Sinica 18(2008), 987-1006



Jianwei Chen and Hulin Wu

San Diego State University and University of Rochester

Abstract: In this paper, we develop local polynomial estimation procedures to fit deterministic dynamic models with a focus on the estimation of time-varying parameters. Three local estimation methods for estimating time-varying parameters are proposed: two-step local linear estimation, two-step local quadratic estimation, and a two-step local hybrid method. Although the proposed estimation methods are applicable for general dynamic models, we establish the asymptotic properties of the proposed estimators for a linear deterministic dynamic model and show that the proposed estimators for linear dynamic models achieve the optimal convergence rate. Simulation studies reveal that the proposed two-step estimation methods perform better than the naive one-step local estimator. An application from an AIDS clinical trial is presented to illustrate the methodologies.

Key words and phrases: Asymptotic conditional bias and variance, deterministic dynamic models, differential equation models, HIV/AIDS, one-step local estimators, two-step local estimators, time-varying parameters.

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